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12.57 (1992)

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Suppose that a cyclic group $A$ of order 4 is a $TI$-subgroup of a finite group $G$.
$\qquad$ a) Does $A$ localize a component $L$ of $G$ if $A$ intersects $L \cdot C(L)$ trivially?
$\qquad$ b) What is the structure of the normal closure of $A$ in the case where $A$ centralizes each component of $G$?

Contributor: A. A. Makhnëv

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